Model description
The model is a sum of a pseudo-Voigt elastic peak (fixed mixing), two Gaussian phonon peaks (breathing, bond-buckling), a resolution-convolved DHO magnon, and a linear background:
Individual Components
1. Elastic Peak (Pseudo-Voigt, fixed mixing)
where $\mu = 0.05$ (fixed), $\text{FWHM}_1 = 0.040$ eV (fixed resolution), and: - $L(E, x_1, \text{FWHM}_1) = \frac{(\text{FWHM}_1/2)^2}{(E - x_1)^2 + (\text{FWHM}_1/2)^2}$ (Lorentzian) - $G(E, x_1, \text{FWHM}_1) = \exp\left(-\frac{(E - x_1)^2}{2\sigma_1^2}\right)$ where $\sigma_1 = \frac{\text{FWHM}_1}{2\sqrt{2\ln(2)}}$ (Gaussian)
2. Breathing Mode (Gaussian)
where $\sigma_2 = \frac{\text{FWHM}_2}{2\sqrt{2\ln(2)}}$ and $\text{FWHM}_2 = 0.040$ eV (fixed resolution)
3. Magnon Peak (DHO convolved with Gaussian resolution)
where $\gamma = \frac{FWHM_3}{2}$ (free parameter), and $G_{\text{res}}(E)$ is a Gaussian with FWHM = 0.040 eV (resolution)
4. Bond-buckling Mode (Gaussian)
where $\sigma_4 = \frac{\text{FWHM}_4}{2\sqrt{2\ln(2)}}$, and $\text{FWHM}_4 = 0.040$ eV (fixed resolution)
5. Linear Background
Fixed Parameters
- Resolution (FWHM) = 0.040 eV for elastic, breathing, and bond-buckling peaks, and for magnon convolution
- Elastic mixing parameter $\mu = 0.05$ (mostly Gaussian with small Lorentzian component)
Free Parameters
- Peak positions: $x_1, x_2, x_3, x_4$ (4 parameters)
- Peak amplitudes: $A_1, A_2, A_3, A_4$ (4 parameters)
- Magnon FWHM: $\text{FWHM}_3$ (1 parameter)
- Background slope: slope (1 parameter)
- Total: 10 free parameters
